AMS 212B Homework, Spring 2016
This homework will help you solidify the bases that you have learnt during the lectures, and test whether you understood them or not. Note that these form a "minimum" set of homeworks. You should try and do as many problems as you can from the textbook as extra practice for the final.
Week 1
- Read and understand further examples given on page 14-17 of textbook.
- Read and understand section 1.3 of textbook.
- Problems 4 and 6 on page 17, Problems 3 and 4 on page 23.
- Answers to Homework 1
Week 2
- Homework 2
- Answers to Homework 2
- Homework 3 . In addition, think about what you would have to do differently if the period of the basic oscillation was not 2pi.
- Answers to Homework 3
Week 4
- Problems 1 and 2 page 131 (answers will be provided for the odd-numbered ones for 2, we can do the even-numbered ones together on Friday).
- Answers to Homework 4 (Note: please ignore the first part of the answers, they were for last year. The answers you are intersted in are in the second part.
- For extra practice on Taylor series: Problems 4.21, 4.22, 4.24 page 147 of RHB. Also, find the Taylor series around x = 1 of exp(x), ln(x), and sin(x)
- Note that you can get the answers on Wolfram alpha.
Week 5
- Questions 1 and 3 of the problem on page 168, and questions 1 and 3 of the problem on page 172.
- Answers to Homework 6
Week 6
- Problems 1 and 2 of this sheet
- Even questions for Problem on page 232, and even questions for problem on page 238.
- Answers to Homework 5
- Answers to Homework 7
Week 7
- Find the two general solutions of the equation 4xf''+2f'+f = 0 using Frobenius series
- Find the two general solutions of the equation xf''+f'- f= 0 using Frobenius series
- The solution can be found on this webpage .
Week 9
- Problem on page 241.
- If you want examples on turning points, do the problem on page 247 with two sets of boundary conditions: (a) y(-1/2) = 0 and y(1/2) = 0, and (b) y(0) = 0 and y(1) = 0.
- Answers to Homework 8
Week 10
- Problem 1 page 261, even problems. Odd problems page 276 (answers are in the book). Problems page 292 (answers are in the book).
- Answers to Homework 9